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+/**
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+ * @author mrdoob / http://mrdoob.com/
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+ * @author alteredq / http://alteredqualia.com/
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+ */
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+
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+THREE.GeometryUtils = {
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+
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+ // Merge two geometries or geometry and geometry from object (using object's transform)
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+
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+ merge: function ( geometry1, geometry2, materialIndexOffset ) {
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+
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+ console.warn( 'THREE.GeometryUtils: .merge() has been moved to Geometry. Use geometry.merge( geometry2, matrix, materialIndexOffset ) instead.' );
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+
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+ var matrix;
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+
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+ if ( geometry2 instanceof THREE.Mesh ) {
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+
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+ geometry2.matrixAutoUpdate && geometry2.updateMatrix();
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+
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+ matrix = geometry2.matrix;
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+ geometry2 = geometry2.geometry;
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+
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+ }
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+
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+ geometry1.merge( geometry2, matrix, materialIndexOffset );
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+
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+ },
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+
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+ // Get random point in triangle (via barycentric coordinates)
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+ // (uniform distribution)
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+ // http://www.cgafaq.info/wiki/Random_Point_In_Triangle
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+
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+ randomPointInTriangle: function () {
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+
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+ var vector = new THREE.Vector3();
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+
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+ return function ( vectorA, vectorB, vectorC ) {
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+
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+ var point = new THREE.Vector3();
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+
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+ var a = THREE.Math.random16();
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+ var b = THREE.Math.random16();
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+
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+ if ( ( a + b ) > 1 ) {
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+
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+ a = 1 - a;
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+ b = 1 - b;
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+
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+ }
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+
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+ var c = 1 - a - b;
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+
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+ point.copy( vectorA );
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+ point.multiplyScalar( a );
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+
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+ vector.copy( vectorB );
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+ vector.multiplyScalar( b );
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+
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+ point.add( vector );
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+
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+ vector.copy( vectorC );
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+ vector.multiplyScalar( c );
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+
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+ point.add( vector );
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+
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+ return point;
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+
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+ };
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+
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+ }(),
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+
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+ // Get random point in face (triangle)
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+ // (uniform distribution)
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+
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+ randomPointInFace: function ( face, geometry, useCachedAreas ) {
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+
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+ var vA, vB, vC;
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+
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+ vA = geometry.vertices[ face.a ];
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+ vB = geometry.vertices[ face.b ];
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+ vC = geometry.vertices[ face.c ];
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+
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+ return THREE.GeometryUtils.randomPointInTriangle( vA, vB, vC );
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+
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+ },
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+
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+ // Get uniformly distributed random points in mesh
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+ // - create array with cumulative sums of face areas
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+ // - pick random number from 0 to total area
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+ // - find corresponding place in area array by binary search
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+ // - get random point in face
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+
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+ randomPointsInGeometry: function ( geometry, n ) {
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+
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+ var face, i,
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+ faces = geometry.faces,
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+ vertices = geometry.vertices,
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+ il = faces.length,
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+ totalArea = 0,
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+ cumulativeAreas = [],
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+ vA, vB, vC, vD;
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+
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+ // precompute face areas
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+
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+ for ( i = 0; i < il; i ++ ) {
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+
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+ face = faces[ i ];
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+
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+ vA = vertices[ face.a ];
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+ vB = vertices[ face.b ];
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+ vC = vertices[ face.c ];
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+
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+ face._area = THREE.GeometryUtils.triangleArea( vA, vB, vC );
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+
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+ totalArea += face._area;
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+
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+ cumulativeAreas[ i ] = totalArea;
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+
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+ }
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+
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+ // binary search cumulative areas array
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+
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+ function binarySearchIndices( value ) {
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+
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+ function binarySearch( start, end ) {
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+
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+ // return closest larger index
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+ // if exact number is not found
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+
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+ if ( end < start )
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+ return start;
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+
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+ var mid = start + Math.floor( ( end - start ) / 2 );
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+
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+ if ( cumulativeAreas[ mid ] > value ) {
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+
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+ return binarySearch( start, mid - 1 );
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+
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+ } else if ( cumulativeAreas[ mid ] < value ) {
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+
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+ return binarySearch( mid + 1, end );
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+
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+ } else {
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+
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+ return mid;
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+
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+ }
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+
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+ }
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+
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+ var result = binarySearch( 0, cumulativeAreas.length - 1 )
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+ return result;
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+
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+ }
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+
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+ // pick random face weighted by face area
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+
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+ var r, index,
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+ result = [];
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+
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+ var stats = {};
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+
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+ for ( i = 0; i < n; i ++ ) {
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+
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+ r = THREE.Math.random16() * totalArea;
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+
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+ index = binarySearchIndices( r );
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+
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+ result[ i ] = THREE.GeometryUtils.randomPointInFace( faces[ index ], geometry, true );
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+
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+ if ( ! stats[ index ] ) {
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+
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+ stats[ index ] = 1;
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+
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+ } else {
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+
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+ stats[ index ] += 1;
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+
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+ }
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+
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+ }
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+
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+ return result;
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+
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+ },
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+
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+ randomPointsInBufferGeometry: function ( geometry, n ) {
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+
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+ var i,
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+ vertices = geometry.attributes.position.array,
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+ totalArea = 0,
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+ cumulativeAreas = [],
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+ vA, vB, vC;
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+
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+ // precompute face areas
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+ vA = new THREE.Vector3();
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+ vB = new THREE.Vector3();
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+ vC = new THREE.Vector3();
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+
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+ // geometry._areas = [];
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+ var il = vertices.length / 9;
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+
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+ for ( i = 0; i < il; i ++ ) {
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+
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+ vA.set( vertices[i * 9 + 0], vertices[i * 9 + 1], vertices[i * 9 + 2] );
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+ vB.set( vertices[i * 9 + 3], vertices[i * 9 + 4], vertices[i * 9 + 5] );
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+ vC.set( vertices[i * 9 + 6], vertices[i * 9 + 7], vertices[i * 9 + 8] );
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+
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+ area = THREE.GeometryUtils.triangleArea( vA, vB, vC );
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+ totalArea += area;
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+
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+ cumulativeAreas.push(totalArea);
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+ }
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+
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+ // binary search cumulative areas array
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+
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+ function binarySearchIndices( value ) {
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+
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+ function binarySearch( start, end ) {
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+
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+ // return closest larger index
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+ // if exact number is not found
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+
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+ if ( end < start )
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+ return start;
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+
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+ var mid = start + Math.floor( ( end - start ) / 2 );
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+
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+ if ( cumulativeAreas[ mid ] > value ) {
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+
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+ return binarySearch( start, mid - 1 );
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+
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+ } else if ( cumulativeAreas[ mid ] < value ) {
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+
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+ return binarySearch( mid + 1, end );
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+
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+ } else {
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+
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+ return mid;
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+
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+ }
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+
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+ }
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+
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+ var result = binarySearch( 0, cumulativeAreas.length - 1 )
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+ return result;
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+
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+ }
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+
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+ // pick random face weighted by face area
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+
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+ var r, index,
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+ result = [];
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+
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+ for ( i = 0; i < n; i ++ ) {
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+
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+ r = THREE.Math.random16() * totalArea;
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+
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+ index = binarySearchIndices( r );
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+
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+ // result[ i ] = THREE.GeometryUtils.randomPointInFace( faces[ index ], geometry, true );
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+ vA.set( vertices[index * 9 + 0], vertices[index * 9 + 1], vertices[index * 9 + 2] );
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+ vB.set( vertices[index * 9 + 3], vertices[index * 9 + 4], vertices[index * 9 + 5] );
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+ vC.set( vertices[index * 9 + 6], vertices[index * 9 + 7], vertices[index * 9 + 8] );
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+ result[ i ] = THREE.GeometryUtils.randomPointInTriangle( vA, vB, vC );
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+
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+ }
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+
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+ return result;
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+
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+ },
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+
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+ // Get triangle area (half of parallelogram)
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+ // http://mathworld.wolfram.com/TriangleArea.html
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+
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+ triangleArea: function () {
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+
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+ var vector1 = new THREE.Vector3();
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+ var vector2 = new THREE.Vector3();
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+
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+ return function ( vectorA, vectorB, vectorC ) {
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+
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+ vector1.subVectors( vectorB, vectorA );
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+ vector2.subVectors( vectorC, vectorA );
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+ vector1.cross( vector2 );
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+
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+ return 0.5 * vector1.length();
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+
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+ };
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+
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+ }(),
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+
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+
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+ ,
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+
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+ center: function ( geometry ) {
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+
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+ console.warn( 'THREE.GeometryUtils: .center() has been moved to Geometry. Use geometry.center() instead.' );
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+ return geometry.center();
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+
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+ }
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+
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+};
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